Most longer tournaments that are open for anyone, usually have multiple schedules that you can play on.
The details from this year's US Open can be found at the following link: http://www.uschess.org/tournaments/2014/usopen/
There was the standard 9-day, a 6-day and 4-day option.
Another place to check is the Continental Chess Association. It appears that maybe the 9 round events, that qualify for norms at least, may not have multiple schedules anymore (something about some FIDE regulations).
World Open: http://www.worldopen.com/ -- The Open on one schedule, the other sections had multiple schedules.
North American Open: http://www.northamericanopen.com/ -- Open is 9 rounds (probably will be one schedule next year) and 7 rounds on the other sections with multiple schedules.
They have some other events also so you would need to look through them to find ones that have more than 6 rounds with multiple schedules. It is possible that the formats may change in future events.
I imagine there are some other groups running long events with multiple schedules too.
If you are just interested in USCF sponsored events (when you mention a national tournament) then the US Open may be the only one.
I am planning on playing in a big national tournament, and the US Open is the only one i know of that has more then six games. I am unable to get more information then when it is being held, though. Does anyone know if thee is an option for playing in a schedule that is less then 9 days? Or how to access more information?